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CS 430 / INFO 430 Information Retrieval. Lecture 11 Latent Semantic Indexing Extending the Boolean Model. Course Administration. Assignment 1 If you have questions about your grading, send me email.

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CS 430 / INFO 430 Information Retrieval

Lecture 11

Latent Semantic Indexing

Extending the Boolean Model

Course Administration

Assignment 1

If you have questions about your grading, send me email.

The following are reasonable requests: the wrong files were graded, points were added up wrongly, comments are unclear, etc.

We are not prepared to argue over details of judgment.

If you ask for a regrade, the final grade may be lower than the original!

Course Administration

Assignment 2

The assignment has been posted.

The test data is being checked. Look for changes before Saturday evening.

Course Administration

Midterm Examination

Wednesday, October 14, 7:30 to 9:00 p.m., Upson B17. Open book.

Laptop computers may be used for lecture slides, notes, readings, etc., but no network connections during the examination.

A sample examination and discussion of the solution will

be posted to the Web site.

CS 430 / INFO 430 Information Retrieval

Latent Semantic Indexing

Latent Semantic Indexing


Replace indexes that use sets of index terms by indexes that use concepts.


Map the term vector space into a lower dimensional space, using singular value decomposition.

Each dimension in the new space corresponds to a latent concept in the original data.

Deficiencies with Conventional Automatic Indexing

Synonymy: Various words and phrases refer to the same concept (lowers recall).

Polysemy: Individual words have more than one meaning (lowers precision)

Independence: No significance is given to two terms that frequently appear together


Query: "IDF in computer-based information look-up"

Index terms for a document:access, document, retrieval,


How can we recognize that informationlook-up is related to retrieval and indexing?

Conversely, if information has many different contexts in the set of documents, how can we discover that it is an unhelpful term for retrieval?

Technical Memo Example: Titles

 c1Human machine interface for Lab ABC computer applications

 c2A survey of user opinion of computer system response time

 c3The EPS user interface management system

 c4System and humansystem engineering testing of EPS

 c5Relation of user-perceived responsetime to error measurement

m1The generation of random, binary, unordered trees

m2The intersection graph of paths in trees

m3Graph minors IV: Widths of trees and well-quasi-ordering

 m4Graph minors: A survey

Technical Memo Example: Terms and Documents















Technical Memo Example: Query


Find documents relevant to "human computer interaction"

Simple Term Matching:

Matches c1, c2, and c4

Misses c3 and c5

The index term vector space


The space has as many dimensions as there are terms in the word list.





Models of Semantic Similarity

Proximity models: Put similar items together in some space or


•Clustering (hierarchical, partition, overlapping). Documents are considered close to the extent that they contain the same terms. Most then arrange the documents into a hierarchy based on distances between documents. [Covered later in course.]

•Factor analysis based on matrix of similarities between documents (single mode).

•Two-mode proximity methods. Start with rectangular matrix and construct explicit representations of both row and column objects.

Selection of Two-mode Factor Analysis

Additional criterion:

Computationally efficient O(N2k3)

N is number of terms plus documents

k is number of dimensions

Figure 1

• term



--- cosine > 0.9

Mathematical concepts

Singular Value Decomposition

Define X as the term-document matrix, with t rows (number of index terms) and d columns (number of documents).

There exist matrices T, S and D', such that:

X = T0S0D0'

T0 and D0 are the matrices of left and right singular vectors

T0 and D0 have orthonormal columns

S0 is the diagonal matrix of singular values

Dimensions of matrices

t x d

t x m

m x m

m x d






m is the rank of X< min(t, d)

Reduced Rank



Diagonal elements of S0 are positive and decreasing in magnitude. Keep the first k and set the others to zero.

Delete the zero rows and columns of S0 and the corresponding rows and columns of T0 and D0. This gives:

X X = TSD'


If value of k is selected well, expectation is that X retains the semantic information from X, but eliminates noise from synonymy,and recognizes dependence.



Selection of singular values

t x d

t x k

k x k

k x d







k is the number of singular values chosen to represent the concepts in the set of documents.

Usually, k« m.

Comparing Two Terms


The dot product of two rows of X reflects the extent to which two terms have a similar pattern of occurrences.



XX' = TSD'(TSD')'


=TSS'T Since D is orthonormal

= TS(TS)'

To calculate thei, jcell, take the dot product between the i and j rows ofTS

Since S is diagonal, TS differs from T only by stretching the coordinate system

Comparing Two Documents


The dot product of two columns of X reflects the extent to which two columns have a similar pattern of occurrences.



X'X = (TSD')'TSD'

= DS(DS)'

To calculate thei, jcell, take the dot product between the i and j columns ofDS.

Since S is diagonal DS differs from D only by stretching the coordinate system

Comparing a Term and a Document

Comparison between a term and a document is the value of an individual cell of X.

X = TSD'

= TS(DS)'

where S is a diagonal matrix whose values are the square root of the corresponding elements of S.






Technical Memo Example: Query

Terms Query















"humansystem interactions on trees"

In term-document space, a query is represented by xq, a t x 1 vector.

In concept space, a query is represented by dq, a 1 x k vector.

Comparing a Query and a Document

A query can be expressed as a vector in the term-document vector space xq.

xqi= 1 if term i is in the query and 0 otherwise.

Let pqj be the inner product of the queryxqwith document dj in the term-document vector space.

pqj is the jth element in the product of xq'X.


Comparing a Query and a Document



[pq1... pqj ... pqt] = [xq1 xq2 ... xqt]

document dj is column j of X


inner product of query q with document dj



pq' = xq'X

= xq'TSD'

= xq'T(DS)'

similarity(q, dj) =

cosine of angle is inner product divided by lengths of vectors


|xq| |dj|

Revised October 6, 2004

Comparing a Query and a Document

In the reading, the authors treat the query as a pseudo-document in the concept space dq:

dq = xq'TS-1

To compare a query against document j, they extend the method used to compare document i with document j.

Take the jth element of the product of:

dqS and(DS)'

This is the jth element of product of:

xq'T (DS)' which is the same expression as before.

Note that dq is a row vector.

Revised October 6, 2004

Experimental Results

Deerwester, et al. tried latent semantic indexing on two test collections, MED and CISI, where queries and relevant judgments available.

Documents were full text of title and abstract.

Stop list of 439 words (SMART); no stemming, etc.

Comparison with:

(a) simple term matching, (b) SMART, (c) Voorhees method.

Experimental Results: 100 Factors

Experimental Results: Number of Factors

CS 430 / INFO 430 Information Retrieval

Extending the Boolean Model

Boolean Diagram

not (A or B)

A and B



A or B

Problems with the Boolean model

Counter-intuitive results:

Query q = A and B and C and D and E

Document d has terms A, B, C and D, but not E

Intuitively, d is quite a good match for q, but it is rejected by the Boolean model.

Query q = A or B or C or D or E

Document d1 has terms A, B, C,D and E

Document d2 has term A, but not B, C,D or E

Intuitively, d1 is a much better match than d2, but the Boolean model ranks them as equal.

Problems with the Boolean model (continued)

Boolean is all or nothing

•Boolean model has no way to rank documents.

•Boolean model allows for no uncertainty in assigning index terms to documents.

•The Boolean model has no provision for adjusting the importance of query terms.

Boolean model as sets

d is either in the set A or not in A.



Extending the Boolean model

Term weighting

•Give weights to terms in documents and/or queries.

•Combine standard Boolean retrieval with vector ranking of results

Fuzzy sets

•Relax the boundaries of the sets used in Boolean retrieval

Ranking methods in Boolean systems

SIRE (Syracuse Information Retrieval Experiment)

Term weights

•Add term weights to documents

Weights calculated by the standard method of

term frequency * inverse document frequency.


• Calculate results set by standard Boolean methods

• Rank results by vector distances

Relevance feedback in SIRE

SIRE (Syracuse Information Retrieval Experiment)

Relevance feedback is particularly important with Boolean

retrieval because it allow the results set to be expanded

• Results set is created by standard Boolean retrieval

• User selects one document from results set

• Other documents in collection are ranked by vector

distance from this document

Boolean model as fuzzy sets

d is more or less in A.



Basic concept

•A document has a term weight associated with each index term. The term weight measures the degree to which that term characterizes the document.

•Term weights are in the range [0, 1]. (In the standard Boolean model all weights are either 0 or 1.)

•For a given query, calculate the similarity between the query and each document in the collection.

•This calculation is needed for every document that has a non-zero weight for any of the terms in the query.

MMM: Mixed Min and Max model

Fuzzy set theory

dAis the degree of membership of an element to set A

intersection (and)

dAB = min(dA, dB)

union (or)

dAB = max(dA, dB)

MMM: Mixed Min and Max model

Fuzzy set theory example

standard fuzzy

set theory set theory



and dAB10000.5000

or dAB11100.70.50.70

MMM: Mixed Min and Max model

Terms: A1, A2, . . . , An

DocumentD, with index-term weights: dA1, dA2, . . . , dAn

Qor = (A1or A2or . . . or An)

Query-document similarity:

S(Qor, D) = Cor1 * max(dA1, dA2,.. , dAn) + Cor2 * min(dA1, dA2,.. , dAn)

where Cor1 + Cor2 = 1

MMM: Mixed Min and Max model

Terms: A1, A2, . . . , An

DocumentD, with index-term weights: dA1, dA2, . . . , dAn

Qand = (A1and A2and . . . and An)

Query-document similarity:

S(Qand, D) = Cand1 * min(dA1,.. , dAn) + Cand2 * max(dA1,.. , dAn)

where Cand1 + Cand2 = 1

MMM: Mixed Min and Max model

Experimental values:

Cand1 in range [0.5, 0.8]

Cor1 > 0.2

Computational cost is low. Retrieval performance much improved.

Other Models

Paice model

The MMM model considers only the maximum and minimum document weights. The Paice model takes into account all of the document weights. Computational cost is higher than MMM.

P-norm model

DocumentD, with term weights: dA1, dA2, . . . , dAn

Query terms are given weights, a1, a2, . . . ,an

Operators have coefficients that indicate degree of strictness

Query-document similarity is calculated by considering each document and query as a point in n space.

Test data





Percentage improvement over standard Boolean model (average best precision)

Lee and Fox, 1988


E. Fox, S. Betrabet, M. Koushik, W. Lee, Extended Boolean Models, Frake, Chapter 15

Methods based on fuzzy set concepts

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